To determine the slope of the line that passes through the points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex], we use the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are coordinates of the two points.
For the points [tex]\( J(1, -4) \)[/tex] and [tex]\( K(-2, 8) \)[/tex]:
- [tex]\(x_1 = 1\)[/tex]
- [tex]\(y_1 = -4\)[/tex]
- [tex]\(x_2 = -2\)[/tex]
- [tex]\(y_2 = 8\)[/tex]
Substitute these values into the slope formula:
[tex]\[
\text{slope} = \frac{8 - (-4)}{-2 - 1}
\][/tex]
Simplifying the expression in the numerator and the denominator, we get:
[tex]\[
\text{slope} = \frac{8 + 4}{-2 - 1} = \frac{12}{-3}
\][/tex]
Further simplifying the fraction:
[tex]\[
\text{slope} = -4
\][/tex]
Thus, the correct answer is [tex]\( A \)[/tex].
